Answer
two real solutions
Work Step by Step
Using the properties of equality, the given quadratic equation, $
3x=-2x^2+7
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2+3x-7=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
2
\\b=
3
\\c=
-7
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(3)^2-4(2)(-7)
\\\\=
9+56
\\\\=
65
.\end{array}
Since the value of the discriminant is $\text{
greater than zero
,}$ then the given quadratic equation has $\text{
two real solutions
}$.